Dessin d’enfant and a description of mutually nonlocal 7-branes without using branch cuts
| Autor: | Naoto Kan, Shun'ya Mizoguchi, Shin Fukuchi, Hitomi Tashiro |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Physical Review |
| ISSN: | 2470-0029 2470-0010 |
| DOI: | 10.1103/physrevd.100.126025 |
| Popis: | We consider the special roles of the zero loci of the Weierstrass invariants g2(τ(z)) and g3(τ(z)) in F theory on an elliptic fibration over P1 or a further fibration thereof. They are defined as the zero loci of the coefficient functions f(z) and g(z) of a Weierstrass equation. They are thought of as complex codimension-1 objects and correspond to the two kinds of critical points of a dessin d’enfant of Grothendieck. The P1 base is divided into several cell regions bounded by some domain walls extending from these planes and D-branes, on which the imaginary part of the J function vanishes. This amounts to drawing a dessin with a canonical triangulation. We show that the dessin provides a new way of keeping track of mutual nonlocalness among 7-branes without employing unphysical branch cuts or their base point. With the dessin, we can see that weak- and strong-coupling regions coexist and are located across an S wall from each other. We also present a simple method for computing a monodromy matrix for an arbitrary path by tracing the walls it goes through. |
| Databáze: | OpenAIRE |
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